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(A) Given: Initial number of nuclei $N_0 = 8 	imes 10^{16}$,half-life $T = 15 	ext{ days}$,and total time $t = 60 	ext{ days}$.First,calculate the

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$7.5 	imes 10^{16}$

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(A) Given: Initial number of nuclei $N_0 = 8 	imes 10^{16}$,half-life $T = 15 	ext{ days}$,and total time $t = 60 	ext{ days}$.First,calculate the number of half-lives $n$:$n = \frac{t}{T} = \frac{60}{15} = 4$.The number of nuclei remaining $N$ after $n$ half-lives is given by:$N = N_0 \left(\frac{1}{2}ight)^n = 8 	imes 10^{16} 	imes \left(\frac{1}{2}ight)^4 = 8 	imes 10^{16} 	imes \frac{1}{16} = 0.5 	imes 10^{16}$.The number of nuclei decayed is the difference between the initial and remaining nuclei:$	ext{Decayed nuclei} = N_0 - N = 8 	imes 10^{16} - 0.5 	imes 10^{16} = 7.5 	imes 10^{16}$.

$A$ sample of a radioactive element contains $8 \times 10^{16}$ active nuclei. The half-life of the element is $15 \text{ days}$. The number of nuclei decayed after $60 \text{ days}$ is:

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